Question

Multiply (7.7 × 10^6)(7 × 10^5). Express the result in scientific notation.

Answer 1

The scientific notation for 5390000000000 = 5.39 x 10^12

Answer 2

Answer:

5.39 × 10¹²

Explanation:

Multiply the coefficients.

7.7 × 7 = 53.9

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Multiply the exponential terms.

When you multiply exponential terms, you add the exponents.

10⁵ × 10⁶ = 10⁽⁵⁺⁶⁾ = 10¹¹

10⁵ × 10⁶ = 10¹¹

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Multiply the products of the coefficients and the exponential terms.

Product = 53.9 × 10¹¹

However, the answer is not in standard form. It should have only one digit before the decimal point.

Product = 53.9 × 10¹¹                   Multiply by 10/10

Product = 53.9 × 10¹¹ × 10/10       Distribute the 10s

Product = (53.9/10) × (10¹¹ × 10)  

Product = 5.39 × 10¹²

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A scientific calculator does the operation for you automatically. The buttons may have different labels on your calculator, but the key sequence is usually something like

7.7 Exp 6 × 7 Exp 5 = 5.39 × 10¹²